Most of this code requires using the Genesis Framework since that is mostly what I work with. So assume that any PHP should go into the child theme's functions file, functions.php (or page template where specified), and style rules go in the style sheet, usually style.css.

To remove an element from your entire website you can simply add the remove_action to your functions.php but when you only want to remove them from certain sections of the site and leave it untouched elsewhere. You add an action that fires on the hook before the element you want to remove and include a conditional statement.
For example if you wanted to keep the post info and post meta from displaying on any posts in categories 1 or 2 you would add:

PHP

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//Remove post-info & post-meta from categories with IDs of 1 & 2

add_action('genesis_before_post','remove_elements');

functionremove_elements(){

if(is_category(array('1','2'))||in_category(array('1','2'))){

remove_action('genesis_before_post_content','genesis_post_info');

remove_action('genesis_after_post_content','genesis_post_meta');

}

}

Or to remove the header and primary navigation from the home page you would use: